Taxonomies of living things and the methods used to produce them changed little with the institutionalization of evolutionary thinking in biology. Instead, the relationships expressed in existing taxonomies were merely reinterpreted as the result of evolution, and evolutionary concepts were developed to justify existing methods. I argue that the delay of the Darwinian Revolution in biological taxonomy has resulted partly from a failure to distinguish between two fundamentally different ways of ordering identified by Griffiths : classification and systematization. Classification consists of ordering entities into classes, groups defined by the attributes of their members; in contrast, systematization consists of ordering entities into systems, more inclusive entities whose existence depends on some natural process through which their parts are related. Evolutionary, or phylogenetic, systematics takes evolutionary descent to be the natural process of interest in biological taxonomy. I outline a general framework for a truly phylogenetic systematics and examine some of its consequences